Public Key Cryptography based on Semigroup Actions

A generalization of the original Diffie-Hellman key exchange in $(\Z/p\Z)^*$ found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general. In Section 2 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system.Comment: 20 pages. To appear in Advances in Mathematics of Communication

Updated results on prototype chalcogenide fibers for 10-um wavefront spatial filtering

The detection of terrestrial planets by Darwin/TPF missions will require extremely high quality wavefronts. Single-mode fibers have proven to be powerful beam cleaning components in the near-infrared, but are currently not available in the mid-infrared where they would be critically needed for Darwin/TPF. In this paper, we present updated measurements on the prototype chalcogenide fibers we are developing for the purpose of mid-infrared spatial filtering. We demonstrate the guiding property of our 3rd generation component and we characterize its filtering performances on a 4 mm length: the far-field radiation pattern matches a Gaussian profile at the level of 3% rms and 13% pk-pk.Comment: 4 pages, 5 figures, to appear in the proceedings of the conference "Toward Other Earths, Darwin/TPF and the search for extrasolar terrestrial planets", held in Heidelberg, Germany, 22-25 April 2003, ESA SP-53

Properties of nitrogen-vacancy centers in diamond: group theoretic approach

We present a procedure that makes use of group theory to analyze and predict the main properties of the negatively charged nitrogen-vacancy (NV) center in diamond. We focus on the relatively low temperatures limit where both the spin-spin and spin-orbit effects are important to consider. We demonstrate that group theory may be used to clarify several aspects of the NV structure, such as ordering of the singlets in the ($e^2$) electronic configuration, the spin-spin and the spin-orbit interactions in the ($ae$) electronic configuration. We also discuss how the optical selection rules and the response of the center to electric field can be used for spin-photon entanglement schemes. Our general formalism is applicable to a broad class of local defects in solids. The present results have important implications for applications in quantum information science and nanomagnetometry.Comment: 30 pages, 6 figure

Monitoring Ion Channel Function In Real Time Through Quantum Decoherence

In drug discovery research there is a clear and urgent need for non-invasive detection of cell membrane ion channel operation with wide-field capability. Existing techniques are generally invasive, require specialized nano structures, or are only applicable to certain ion channel species. We show that quantum nanotechnology has enormous potential to provide a novel solution to this problem. The nitrogen-vacancy (NV) centre in nano-diamond is currently of great interest as a novel single atom quantum probe for nanoscale processes. However, until now, beyond the use of diamond nanocrystals as fluorescence markers, nothing was known about the quantum behaviour of a NV probe in the complex room temperature extra-cellular environment. For the first time we explore in detail the quantum dynamics of a NV probe in proximity to the ion channel, lipid bilayer and surrounding aqueous environment. Our theoretical results indicate that real-time detection of ion channel operation at millisecond resolution is possible by directly monitoring the quantum decoherence of the NV probe. With the potential to scan and scale-up to an array-based system this conclusion may have wide ranging implications for nanoscale biology and drug discovery.Comment: 7 pages, 6 figure

Mu-Metal Enhancement of Effects in Electromagnetic Fields Over Single Emitters Near Topological Insulators

We focus on the transmission and reflection coefficients of light in systems involving of topological insulators (TI). Due to the electro-magnetic coupling in TIs, new mixing coefficients emerge leading to new components of the electromagnetic fields of propagating waves. We have discovered a simple heterostructure that provides a 100-fold enhancement of the mixing coefficients for TI materials. Such effect increases with the TI's wave impedance. We also predict a transverse deviation of the Poynting vector due to these mixed coefficients contributing to the radiative electromagnetic field of an electric dipole. Given an optimal configuration of the dipole-TI system, this deviation could amount to $0.18\%$ of the Poynting vector due to emission near not topological materials, making this effect detectable